Frequency Offset Estimation in Orthogonal Frequency Division Multiple Access Wireless Networks

ABSTRACT

A method of wireless transmission for estimating the carrier frequency offset in a base station of a received transmission from a user equipment (UE) accessing a radio access network. The method time de-multiplexes selected symbols of a received sub-frame, computes the frequency-domain symbols received from each antenna through an FFT, de-maps the UEs selected sub-carriers for each antenna, computes metrics associated to a carrier frequency offset hypothesis spanning a searched frequency offset window, repeats these steps on subsequent received sub-frames from the UE over an estimation interval duration, non-coherently accumulates the computed metrics and selects the carrier frequency offset hypothesis with largest accumulated metric amplitude.

CLAIM OF PRIORITY

This application claims priority under 35 U.S.C. 119(e)(1) to U.S.Provisional Application No. 61/079,933 filed Jul. 11, 2008, U.S.Provisional Application No. 61/095,405 filed Sep. 9, 2008 and U.S.Provisional Application No. 61/100,104 filed Sep. 25, 2008.

TECHNICAL FIELD OF THE INVENTION

The technical field of this invention is wireless communication.

BACKGROUND OF THE INVENTION

FIG. 1 shows an exemplary wireless telecommunications network 100. Theillustrative telecommunications network includes base stations 101, 102and 103, though in operation, a telecommunications network necessarilyincludes many more base stations. Each of base stations 101, 102 and 103are operable over corresponding coverage areas 104, 105 and 106. Eachbase station's coverage area is further divided into cells. In theillustrated network, each base station's coverage area is divided intothree cells. Handset or other user equipment (UE) 109 is shown in Cell A108. Cell A 108 is within coverage area 104 of base station 101. Basestation 101 transmits to and receives transmissions from UE 109. As UE109 moves out of Cell A 108 and into Cell B 107, UE 109 may be handedover to base station 102. Because UE 109 is synchronized with basestation 101, UE 109 can employ non-synchronized random access toinitiate handover to base station 102.

Non-synchronized UE 109 also employs non-synchronous random access torequest allocation of up-link 111 time or frequency or code resources.If UE 109 has data ready for transmission, which may be traffic data,measurements report, tracking area update, UE 109 can transmit a randomaccess signal on up-link 111. The random access signal notifies basestation 101 that UE 109 requires up-link resources to transmit the UEsdata. Base station 101 responds by transmitting to UE 109 via down-link110, a message containing the parameters of the resources allocated forUE 109 up-link transmission along with a possible timing errorcorrection. After receiving the resource allocation and a possibletiming advance message transmitted on down-link 110 by base station 101,UE 109 optionally adjusts its transmit timing and transmits the data onup-link 111 employing the allotted resources during the prescribed timeinterval.

Long Term Evolution (LTE) wireless networks, also known as EvolvedUniversal Terrestrial Radio Access Network (E-UTRAN), are beingstandardized by the 3GPP working groups (WG). Orthogonal frequencydivision multiple access (OFDMA) and SC-FDMA (single carrier FDMA)access schemes were chosen for the down-link (DL) and up-link (UL) ofE-UTRAN, respectively. User Equipments (UEs) are time and frequencymultiplexed on a physical uplink shared channel (PUSCH) and time andfrequency synchronization between UEs guarantees optimal intra-cellorthogonality. In UL, frequency offsets (FO) can be due to localoscillator (LO) drifts at both the UE and the Base Station, alsoreferred to as eNodeB, but also to the UE speed translating into Dopplershift in line of sight (LOS) propagation conditions. If the largesub-carrier spacing of LTE (15 kHz) makes it robust with respect toorthogonality loss due to Doppler shift, since even high speed trainswould not generate a Doppler shift exceeding one tenth of a sub-carrier,the frequency offset still has a negative impact on BLER due to fastchannel variation within a sub-frame:

Rayleigh TU channel: FO range of 0 to 300 Hz with the maximum frequencyinaccuracies at eNB of 0.05 ppm and at UE of 0.1 ppm;

AWGN (LOS) channel: FO range of 0 to 1600 Hz with the UE speedtranslating into Doppler shift.

FIG. 2 shows the BLER performance degradation due to various frequencyoffsets with quadrature phase shift keying (QPSK) modulation and turbocoding rate of ⅓ with AWGN. FIG. 3 similarly shows the BLER performancedegradation with TU-6 fading channel. There is a need to estimate andremove the frequency offset before channel estimation and demodulation.This invention is a frequency estimation method which applies directlyon the de-mapped frequency sub-carriers of a UEs symbol and compares itsperformance with other published methods.

On top of these scenarios, the 3GPP Working Group #4 defined propagationchannels specifically addressing the frequency offset estimation andcompensation function which worst-case scenarios are expected to beencountered along High Speed Trains (HST) lines. FIG. 4 illustrates thefrequency offset time behavior of both channels. FIG. 5 illustrates theresulting frequency variations observed within a 30 ms interval.

In an additional channel scenario, Rician fading is considered whereRician factor K=10 dB is the ratio between the dominant signal power andthe variant of the other weaker signals.

It is clear from FIGS. 4 and 5 that in order to track the abruptfrequency offset variations of the HST scenarios, the eNB mustpermanently estimate the frequency offset of each UE. This patentapplication assumes the following scheme for concurrent frequency offsetestimation and compensation illustrated in FIG. 6. In FIG. 6 frequencyestimation is performed for a given UE during an estimation interval 610and a frequency estimate is issued at the end of interval 610. During agiven estimation interval 620 of a given UE, the frequency estimateissued by the previous interval 610 is replaced.

SUMMARY OF THE INVENTION

This patent application details the design choices for the LTE frequencyoffset estimation and compensation, from theoretical derivations andperformance evaluations. It is shown that the state-of-the-art does notsatisfactorily addresses the high-end performance requirements of LTE sothat an alternate approach is needed. This invention is amaximum-likelihood based solution using the available frequency-domaininterference-free symbols de-mapped (or de-multiplexed) at the output ofthe Fast Fourier Transform (FFT) of an OFDMA multi-user receiver. Theestimator operates on frequency-domain OFDMA user symbols extracted froman OFDMA multiplex with sub-carrier modulation is known a-priori. Othersolutions either rely on pilot repetition or on an interference-freecyclic prefix (CP) not used in OFDMA systems such as LTE.

BRIEF DESCRIPTION OF THE DRAWINGS

These and other aspects of this invention are illustrated in thedrawings, in which:

FIG. 1 is a diagram of a communication system of the prior art relatedto this invention having three cells;

FIG. 2 illustrates the BLER performance degradation due to variousfrequency offsets with quadrature phase shift keying (QPSK) modulationand turbo coding rate of ⅓ with AWGN;

FIG. 3 is similar to FIG. 2 and illustrates the BLER performancedegradation with TU-6 fading channel;

FIG. 4 illustrates the frequency offset time behavior of two channeltypes;

FIG. 5 illustrates the resulting frequency variations in these twochannel types observed within a 30 ms interval;

FIG. 6 illustrates the invention for concurrent frequency offsetestimation and compensation;

FIG. 7 illustrates the principles of the single carrier frequencydivision multiple access (SC-FDMA) UL transmitter and receiver of LTE;

FIG. 8 illustrates two ways to remove the frequency offset oncefrequency offset compensation has been estimated;

FIG. 9 illustrates the number of complex multiples required for varioustime and frequency-domain FO compensation methods for the full range ofallocated RBs per UE;

FIG. 10 illustrates a maximum-likelihood algorithm which tests a numberof frequency offset hypothesis on the demodulation reference symbols(DMRS) located at the centre of each slot according to this invention;

FIG. 11 illustrates computing the metric M(δf) by multiplying thereceived de-mapped FFT output samples R_(S)(k) with the complexconjugate of frequency shifted replicas of the expected DMRSfrequency-domain sequence S(k,δf_(i));

FIG. 12 illustrates computing the metric M(δf) by multiplying thefrequency shifted replicas of the received de-mapped FFT output sampleR_(S(k),δf_(i)) with the complex conjugate of the expected DMRS sequenceS(k);

FIG. 13 illustrates the continuous frequency signal of a DMRS sequence(Drifted Symbol) and specifically an extended Zadoff-Chu sequence (EZC);

FIG. 14 illustrates the corresponding bias of the FO estimatorillustrated in FIG. 13;

FIG. 15 illustrates the residual bias of a compensated estimator;

FIG. 16 illustrates that the frequency-bins with common channelestimation method can be mapped onto a parabola;

FIG. 17 illustrates that the frequency-bins with per-bin channelestimation method can be mapped onto a parabola;

FIG. 18 is a flow chart illustrating the frequency offset estimation andcompensation algorithm of this invention; and

FIG. 19 illustrates the time behavior of the frequency elementaryestimates within an estimation interval obtained from simulation.

DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS

FIG. 7 illustrates the principles of the single carrier frequencydivision multiple access (SC-FDMA) UL transmitter and receiver of LTE.The SC-FDMA scheme is also referred to as discrete Fourier transformspread orthogonal frequency division multiplexing (DFT-SOFDM) and is anOFDMA system with subband carrier assignment scheme (CAS). For the UEtransmitter coder 711 encodes received modulated symbols. These aretransformed into the frequency domain by discrete Fourier transform(DFT) 712. These are filtered by filter 713. Block 714 combines thesymbols with zeros to fill particular slots. Block 715 is an inverseFast Fourier Transform (IFFT) which converts back into the time domain.Block 716 adds the cyclic prefix (CP) for transmission via the antenna(TxRF). For the base station (eNB) receiver block 721 removes the cyclicprefix. Block 722 is a Fast Fourier Transform (FFT). Filter 723separates the channels corresponding to separate UEs. Processingcontinues with one channel for each active UE. FIG. 7 illustrates twochannels. The two channels include filters 734 and 754. Blocks 735 and755 perform channel estimation and compensation. Following filters 736and 756, blocks 737 and 757 return to the time domain by an inversediscrete Fourier transform (IDFT). Filters 738 and 758 drive respectivedemodulators 739 and 759 which recover the originally transmittedsignals.

FIG. 7 assumes no frequency offset so frequency offset compensation isnot shown. FIG. 8 illustrates two ways to remove the frequency offsetonce frequency offset compensation has been estimated at the basestation receiver: time-domain frequency offset compensation 810; andfrequency-domain frequency offset compensation 820. In time-domainfrequency offset compensation block 811 removes the cyclic prefix fromthe received signals. A bank of frequency compensating filters 812 foreach active UE frequency compensates by e^(−j2πf(i)t). Block 813converts this into the frequency domain via a Fast Fourier Transform(FFT). Filter 814 separates the signals corresponding to the individualUEs 815. In frequency-domain frequency offset compensation block 821removes the cyclic prefix. Block 722 converts into the frequency domainvia a Fast Fourier Transform (FFT). Filter 823 separates thecorresponding to the individual UEs. Each UE channel includes filters834 and 835, a frequency domain interpolation 835 and 855 to generatethe individual UE signals 836 and 856.

The frequency-domain interpolation FIG. 8 820 operates on de-mappedfrequency sub-carriers of a given UE as follows:

$\begin{matrix}{{Z_{i}\left( {k,ɛ} \right)} = {\frac{1}{N_{FFT}}{\sum\limits_{l = 0}^{N_{{sc} - 1}}{{Z(l)}{C\left( {{l - k},ɛ} \right)}}}}} & (1)\end{matrix}$

where: N_(FFT) is the FFT size; N_(SC) is the UE allocation size insub-carriers; ε is the normalized frequency shift equal to δf/Δf_(sc);C(l−k,ε) are the interpolator coefficients; Z_(i)(k,ε) is theinterpolated point from the Z(l) points. Further:

$\begin{matrix}{{C\left( {k,ɛ} \right)} = {\frac{\sin \; {\pi \left( {k + ɛ} \right)}}{\sin \left( {{\pi \left( {k + ɛ} \right)}/N_{FFT}} \right)}^{{{j\pi}{({k + ɛ})}}\frac{N_{FFT} - 1}{N_{FFT}}}}} & (2)\end{matrix}$

According to the expression of Equation (1) this method is also calledfrequency offset compensation through circular convolution. This isderived as follows. Let Z(k), k=0 . . . N_(SC)−1 be the frequencycomplex samples at the DFT output of the UE transmitter in FIG. 7. TheZ(k) samples are mapped onto a wideband signal Z_(WB)(k) as:

$\begin{matrix}{{Z_{WB}(k)} = \left\{ \begin{matrix}{{Z\left( {k - k_{1}} \right)};} & {{k = k_{1}},{k_{1} + 1},\ldots \mspace{14mu},{k_{1} + N_{SC} - 1}} \\0 & {elsewhere}\end{matrix} \right.} & (3)\end{matrix}$

This signal is then converted into the time domain for transmission. Thecyclic prefix plays no role in this derivation so it is omitted withoutloss of generality. This conversion is as follows:

$\begin{matrix}\begin{matrix}{{z_{WB}(n)} = {\frac{1}{\sqrt{N_{FFT}}}{\sum\limits_{k = 0}^{N_{FFT} - 1}{{Z_{WB}(k)}^{{j2}\; \pi \; {{kn}/N_{FFT}}}}}}} \\{= {\frac{1}{\sqrt{N_{FFT}}}{\sum\limits_{k = 0}^{N_{SC} - 1}{{Z(k)}^{{j2}\; \pi \; {({k + k_{1}})}{n/N_{FFT}}}}}}} \\{= {\frac{^{{j2}\; \pi \; {{nk}_{1}/N_{FFT}}}}{\sqrt{N_{FFT}}}{\sum\limits_{k = 0}^{N_{SC} - 1}{{Z(k)}^{{j2}\; \pi \; {{kn}/N_{FFT}}}}}}}\end{matrix} & (4)\end{matrix}$

The normalized frequency offset

${ɛ = \frac{\delta \; f}{f_{sc}}},$

where δf is the frequency offset (Hz) and f_(sc) is the sub-carrierspacing, applies to the time domain signal as:

$\begin{matrix}\begin{matrix}{{z_{{WB} - {FO}}\left( {n,ɛ} \right)} = {{z_{WB}(n)}^{{j2\pi}\; n\; {ɛ/N_{FFT}}}}} \\{= {\frac{^{{j2}\; \pi \; {{nk}_{1}/N_{FFT}}}}{\sqrt{N_{FFT}}}{\sum\limits_{k = 0}^{N_{SC} - 1}{{Z(k)}^{{j2}\; {\pi(\; {k + ɛ})}{n/N_{FFT}}}}}}}\end{matrix} & (5)\end{matrix}$

At the receiver, the frequency domain signal Z_(WB-FO) is obtained byapplying an FFT to z_(WB-FO):

$\begin{matrix}\begin{matrix}{{Z_{{WB} - {FO}}\left( {k,ɛ} \right)} = {\frac{1}{\sqrt{N_{FFT}}}{\sum\limits_{n = 0}^{N_{FFT} - 1}{{z_{{WB} - {FO}}\left( {n,ɛ} \right)}^{{- {j2}}\; \pi \; {{kn}/N_{FFT}}}}}}} \\{= {\frac{1}{N_{FFT}}\sum\limits_{n = 0}^{N_{FFT} - 1}}} \\{{\left\lbrack {\sum\limits_{l = 0}^{N_{SC} - 1}{{Z(l)}^{{j2}\; \pi \; {({l + k_{1} + ɛ})}{n/N_{FFT}}}}} \right\rbrack ^{{- {j2\pi}}\; {{kn}/N_{FFT}}}}} \\{= {\frac{1}{N_{FFT}}{\sum\limits_{l = 0}^{N_{SC} - 1}{{Z(l)}{\sum\limits_{n = 0}^{N_{FFT} - 1}^{{j2}\; \pi \; {({l + k_{1} - k + ɛ})}{n/N_{FFT}}}}}}}}\end{matrix} & (6)\end{matrix}$

Finally, the de-mapped signal Z_(FO)(s, ε) is extracted from Z_(WB-FO)as follows:

$\begin{matrix}{\begin{matrix}{{{Z_{FO}\left( {s,ɛ} \right)} = {Z_{{WB} - {FO}}\left( {{k = {k_{1} + s}},ɛ} \right)}};{s = {{0\mspace{14mu} \ldots \mspace{14mu} N_{SC}} - 1}}} \\{= {\frac{1}{N_{FFT}}{\sum\limits_{l = 0}^{N_{SC} - 1}{{Z(l)}{\sum\limits_{n = 0}^{N_{FFT} - 1}^{{{j2\pi}{({l - s + ɛ})}}{n/N_{FFT}}}}}}}} \\{= {\frac{1}{N_{FFT}}{\sum\limits_{l = 0}^{N_{sc} - 1}{{Z(l)}{C\left( {{l - s},ɛ} \right)}}}}}\end{matrix}{{where}\text{:}}} & (7) \\\begin{matrix}{{C\left( {k,ɛ} \right)} = {\sum\limits_{n = 0}^{N_{FFT} - 1}^{{j2\pi}\; {{n{({k + ɛ})}}/N_{FFT}}}}} \\{= {\frac{\sin \; {\pi \left( {k + ɛ} \right)}}{\sin \left( {{\pi \left( {k + ɛ} \right)}/N_{FFT}} \right)}^{{{j\pi}{({k + ɛ})}}\frac{N_{FFT} - 1}{N_{FFT}}}}}\end{matrix} & (8)\end{matrix}$

The interpolation coefficients apply directly onto the demapped symbolsub-carriers and are not dependent on the UE location in the frequencymultiplex, here modelled by the origin k₁ of the user's sub-carriermapping. Thus once the frequency offset is known at the receiver, thesame set of coefficients can be used for a given UE and allocation sizeirrespective of its sub-carrier mapping. The coefficient set for smallernumber of sub-carriers allocation is a sub-set of the coefficient set oflarger number of sub-carriers allocation. The set of interpolatorcoefficients for a given frequency offset can be computed once for thelargest allocation size and stored in a look up table (LUT) to be usedfor smaller allocation sizes. For example for a 20 MHz LTE spectrum, themaximum allocation is 1200 sub-carriers so that the storage requirementsfor the interpolator of a given UE is 1200 complex coefficients, each of2 by 16 bits for a total of 4.69 KBytes.

Table 1 assumes a 20 MHz LTE spectrum, with the following numerologyfrom 3GPP TS 36.211 v8.1.0 2007-11 standard.

TABLE 1 Symbol duration 66.67 μs Spectrum 20 MHz BW efficiency 90%Sampling rate 30.72 Msps Sub-carrier 15 kHz size FFT size 2048 RB size12 subcarriers = 180 kHz Number of RBs 100

Table 2 is an example of complexity comparison in the number of complexmultiplications. Table 2 lists the number of complex multiples requiredfor various time and frequency-domain FO compensation methods. Table 2assumes 50 UEs each with two allocated resource blocks (RBs) frequencymultiplexed in a 20 MHz symbol. The complexity of the radix-4 FFT istaken as 3*N_(FFT)/4*(ln(N_(FFT))/ln(4)) and the complexity of thefrequency domain FO compensation is taken as N_(SC) ². FIG. 9illustrates this comparison for the full range of allocated RBs per UE.

TABLE 2 Number of Time domain Frequency domain complex TD freq radix-4radix-4 FD freq multiplies comp FFT FFT comp. Common to 8448 all UEs PerUE 2048 8448 576 Sub-total 102400 844800 8448 28800 Total 947200 37248

Table 2 and FIG. 9 show frequency-domain FO compensation is moreefficient than the time-domain FO compensation when the number ofmultiplexed UEs per symbol exceeds about 10% of the multiplexingcapacity.

In OFDMA and SC-FDMA systems such as LTE, the estimated UL frequencyoffset of each multiplexed UE in an OFDM or SC-FDMA symbol is removed infrequency domain after sub-carrier de-mapping by means of the frequencydomain interpolator defined in Equations (1) and (2).

The interpolation coefficients apply directly onto the demapped symbolsub-carriers. The are not dependent on the UE location in the frequencymultiplex. Therefore the same set of coefficients can be used for agiven UE and allocation size irrespective of its sub-carrier mapping.

The coefficient set for smaller number of sub-carriers allocation is asub-set of the coefficient set of larger number of sub-carriersallocation. Thus the set of interpolator coefficients for a givenfrequency offset can be computed once for the largest allocation sizeand stored in a LUT to be used for smaller allocation sizes.

Most algorithms published on the topic of frequency offset estimation inOFDM systems are variations of the Correlation Based method that can beused both in time and frequency domains. Let z, be a sequence of timedomain complex samples such that some of these samples are duplicated intime:

z_(n+LN)=z_(n) ; n=0,1, . . . , N−1; N,L integers  (9)

This sequence is transmitted over the air and received distorted at thedemodulator unit by AWGN samples w_(n) and a frequency offset δf:

r _(n) =z _(n) e ^(j2πnδf/f) ^(s) +w _(n)  (10)

where: f_(s) is the sampling rate. The correlation p in time of thereceived repeated samples is:

$\begin{matrix}{\rho = {\sum\limits_{n = 0}^{N - 1}{r_{n}r_{n + {LN}}^{*}}}} & (11)\end{matrix}$

with a statistical average of:

$\begin{matrix}{{\langle\rho\rangle} = {^{{- j}\; 2\pi \; {LN}\; \delta \; {f/f_{s}}}{\sum\limits_{n = 0}^{N - 1}{z_{n}}^{2}}}} & (12)\end{matrix}$

A non-biased estimator for the normalized frequency offset ε=N δf/f_(s)is:

$\begin{matrix}{\hat{ɛ} = {- \frac{\angle\rho}{2\pi \; L}}} & (13)\end{matrix}$

The same estimator can be derived in frequency domain as follows. TheN-length FFT R_(k) of the received samples r_(n) is:

$\begin{matrix}{R_{k} = {{\frac{1}{\sqrt{N}}{\sum\limits_{n = 0}^{N - 1}{r_{n}^{{- j}\; 2\; \pi \; {{nk}/N}}}}} = {{\frac{1}{\sqrt{N}}{\sum\limits_{n = 0}^{N - 1}{z_{n}^{{- j}\; 2\; \pi \; {{n{({k - ɛ})}}/N}}}}} + w_{n}^{\prime}}}} & (14)\end{matrix}$

where: w_(n)′ are AWGN samples with same statistical properties asw_(n). Similarly, the N-length FFT R_(k)′ of the received samplesr_(n+LN) is:

$\begin{matrix}\begin{matrix}{R_{k}^{\prime} = {\frac{1}{\sqrt{N}}{\sum\limits_{n = 0}^{N - 1}{r_{n + {LN}}^{{- j}\; 2\; \pi \; {{nk}/N}}}}}} \\{= {{\frac{^{j\; 2\pi \; L\; ɛ}}{\sqrt{N}}{\sum\limits_{n = 0}^{N - 1}{z_{n}^{{- j}\; 2\; \pi \; {{n{({k - ɛ})}}/N}}}}} + w_{n + {LN}}^{\prime}}}\end{matrix} & (15)\end{matrix}$

The correlation Γ in time of the received and FFTed repeated samples is:

$\begin{matrix}{\Gamma = {\sum\limits_{k = 0}^{N - 1}{R_{k}R_{k}^{\prime*}}}} & (16)\end{matrix}$

with a statistical average of:

$\begin{matrix}{{\langle\Gamma\rangle} = {^{{j2\pi}\; L\; ɛ}{\sum\limits_{k = 0}^{N - 1}{R_{k}}^{2}}}} & (17)\end{matrix}$

so that a non-biased estimator for the normalized frequency offset ε isgiven by:

$\begin{matrix}{\hat{ɛ} = {- \frac{\angle \; \Gamma}{2\pi \; L}}} & (18)\end{matrix}$

This derivation assumes the same (flat) channel over the two correlatedsymbols and any unpredictable phase variation in between would lead to awrong estimate in equation (18). Therefore the time interval between thecorrelated symbols should be small enough to fulfill this requirement.

This method is especially attractive for its low-complexity when appliedto OFDM systems because it can make use of either the repeated referencesymbols or the inherent duplication of the OFDM symbol tail in thecyclic prefix. FIG. 10 illustrates the sub-frame structure defined inthe LTE standard. The sub-frame includes two 0.5 ms slots (slot 1 andslot 2). Each slot includes six DFT-SOFDM (also denoted as SC-FDMA) datasymbols and one central reference symbol. Both the cyclic prefix (CP)correlation of each symbol and the reference symbols correlation areused in a combined estimator.

For each UE two de-mapped reference symbols of each sub-frame arecorrelated in the frequency domain. The LTE specification allows forboth intra sub-frame frequency hopping and sequence hopping in either abase sequence, a cyclic shift or both. In intra sub-frame frequencyhopping the sequence of the reference symbol changes from one slot toanother. Therefore the symbol cannot be considered anymore as a repeatedsymbol. In sequence hopping the flat channel assumption of the estimatorof equation (18) is violated and the method cannot be used. Thereforefor most cases the reference symbol correlation method is impracticalfor LTE.

Denote r(n) a received OFDM symbol including the CP illustrated in FIG.10 for samples n=0, 1, . . . , N_(FFT)+N_(CP)−1, where N_(FFT) is theFFT size and N_(CP) is the CP length. The frequency domain correlationmethod requires converting both the CP and the corresponding tail of thesymbol in frequency domain to perform the correlation of equation 16.However this can be derived from the already available FFT of thecomplete symbol. This saves performing an additional FFT.

Denote R_(CP)(k) as the FFTs of the CP:

$\begin{matrix}{{R_{CP}(k)} = {\sum\limits_{n = 0}^{N_{CP} - 1}{{r(n)}^{{- j}\; 2\; {{\pi {kn}}/N_{FFT}}}}}} & (19)\end{matrix}$

Denote R_(Tail)(k) as the tail of the OFDM symbol:

$\begin{matrix}{{R_{Tail}(k)} = {\sum\limits_{n = 0}^{N_{CP} - 1}{{r\left( {n + N_{FFT}} \right)}^{{- j}\; 2\; {{\pi {kn}}/N_{FFT}}}}}} & (20)\end{matrix}$

Denote R_(S)(k) as the complete OFDM symbol:

$\begin{matrix}\begin{matrix}{{R_{S}(k)} = {\sum\limits_{n = 0}^{N_{FFT} - 1}{{r\left( {n + N_{CP}} \right)}^{{- j}\; 2\; {{\pi {kn}}/N_{FFT}}}}}} \\{= {{\sum\limits_{n = 0}^{N_{FFT} - N_{CP} - 1}{{r\left( {n + N_{CP}} \right)}^{{- j}\; 2\; {{\pi {kn}}/N_{FFT}}}}} +}} \\{{\sum\limits_{n = {N_{FFT} - N_{CP}}}^{N_{FFT} - 1}{{r\left( {n + N_{CP}} \right)}^{{- j}\; 2\; {{\pi {kn}}/N_{FFT}}}}}}\end{matrix} & (21)\end{matrix}$

The relevant term reflecting the OFDM tail in is the second term, whichcan be re-written as:

$\begin{matrix}\begin{matrix}{{R_{S - {Tail}}(k)} = {\sum\limits_{m = 0}^{N_{CP} - 1}{{r\left( {m + N_{FFT}} \right)}^{{- j}\; 2\; {\pi {({m - N_{CP} + N_{FFT}})}}{k/N_{FFT}}}}}} \\{= {{R_{Tail}(k)}^{j\; 2\pi \; k\; {N_{CP}/N_{FFT}}}}}\end{matrix} & (22)\end{matrix}$

To compensate for the phase difference between the desired R_(Tail)(k)and the available R_(S), R_(CP)(k) must be weighted by e^(j2πkN) ^(CP)^(/N) ^(FFT) before correlating with R_(S)(k) and the correlation inequation (16) is computed as:

$\begin{matrix}{\Gamma = {\sum\limits_{k = 0}^{N_{SC} - 1}{{R_{S}\left( {k + k_{0}} \right)}{R_{CP}^{*}\left( {k + k_{0}} \right)}^{{- j}\; 2\pi \; k\; {N_{CP}/N_{FFT}}}}}} & (23)\end{matrix}$

where: N_(SC) is the number of allocated sub-carriers starting fromsub-carrier k₀. Simulations verify that this implementation optimizationdoes not cause any performance degradation compared with using the FFTof only the tail of the OFDM symbol R_(Tail)(k).

This method was originally designed for OFDM systems where only one UEoccupies the spectrum at a time. In that case both the CP and the OFDMsymbol are free of interference. In OFDMA systems the CP is notinterference-free because, unlike the OFDM symbol, its spectrum is notlimited to the UEs allocated sub-carriers. The CP spectrums spills overadjacent sub-carriers where other UEs are expected to be scheduled.

Simulation results show that this CP interference results in estimationerrors proportional to the frequency offset. Thus the frequencyestimates must be used to compensate the frequency offset beforecomputing a new estimation. The only practical method for frequencycompensation in OFDMA systems operates in frequency domain on thesub-carriers allocated to the UE. There are two options for the CP:remove the frequency offset on the de-mapped sub-carriers; or remove thefrequency offset on the full bandwidth. Removing the frequency offset onthe de-mapped sub-carriers is obviously the more attractive from acomplexity standpoint. However this truncates the frequency-domain CP,thus resulting in erroneous frequency correction. Removing the frequencyoffset on the full bandwidth performs an exact frequency correction inabsence of any interferer. However, this method suffers frominterference as soon as other UEs are multiplexed in the same symbol.Frequency-domain frequency offset generation or compensation methodprovide exactitude when applied to the OFDM symbol because the Driftedand Interpolated symbol provide results similar to each other.

Thus despite the low complexity of the CP-correlation method, a higherperformance method is needed to estimate each UE's frequency offset inLTE. This invention uses the available frequency-domaininterference-free symbols de-mapped (or de-multiplexed) at the output ofthe FFT of an OFDMA multi-user receiver.

The criterion to design a frequency offset estimation algorithm for LTEis that it should circumvent the drawbacks of the state of the artmethods. The new method should only operate on the de-mappedinterference-free OFDM symbols. The new method should not rely on symbolrepetition.

This invention is a maximum-likelihood algorithm which tests a number offrequency offset hypothesis on the demodulation reference symbols (DMRS)located at the center of each slot as shown in FIG. 10. This isexpressed as:

$\begin{matrix}{{\hat{\Delta}\; f} = {\arg \; {\max\limits_{\delta \; f}\left\{ {M\left( {\delta \; f} \right)} \right\}}}} & (24)\end{matrix}$

where: the metric M(δf) can be computed in a number of ways. A firstM(δf) computation multiplies the received de-mapped FFT output samplesR_(S)(k) with the complex conjugate of frequency shifted replicas of theexpected DMRS frequency-domain sequence S(k, δf_(i)):

$\begin{matrix}{{M\left( {\delta \; f} \right)} = {{\sum\limits_{k = 0}^{N_{sc} - 1}{{R_{S}(k)}{S^{*}\left( {k,{\delta \; f}} \right)}}}}} & (25)\end{matrix}$

A second M(δf) computation multiplies the frequency shifted replicas ofthe received de-mapped FFT output sample R_(S(k), δf_(i)) with thecomplex conjugate of the expected DMRS sequence S(k):

$\begin{matrix}{{M\left( {\delta \; f} \right)} = {{\sum\limits_{k = 0}^{N_{sc} - 1}{{R_{S}\left( {k,{\delta \; f}} \right)}{S^{*}(k)}}}}} & (26)\end{matrix}$

FIGS. 11 and 12 illustrate the principles of these two approaches. InFIG. 11 the received sampled are divided into frequency bins in binfilter 1101. The binned signals are converted to frequency domain viaFast Fourier Transform (1102). Filter 1103 separates the signalscorresponding to individual active UEs in exemplary channel 1104.Multiplier 1105 multiplies the channel signal by the processed DMRSsequence via block 1105. Block 1107 performs the required summation andblock 1108 finds the maximum. FIG. 12 operates similarly except the DMRSsignal S(k) 1201 is subject to the frequency bins in block 1202. This isprocessed in block 1203 for multiplication by the correspondingseparated channel signal in multiplier 1106.

Both approaches can be simplified using the frequency-domain frequencyoffset generation or compensation method to build the frequency bins.The two approaches are equivalent in performance-wise. This applicationdescribes the first approach. For DMRS sequence planning with hoppingdisabled, the frequency bins S*(k,δf) of a given UEs DMRS sequence canbe pre-computed and stored in a LUT. Enabling sequence hopping mightresult in a reduced set of expected sequences per UE where the LUTapproach is also beneficial. For the worst-case cell configuration whereDMRS sequences change on every slot (known as base sequence grouphopping) for a given slot S(k,δf) is the same for all UEs.

FIG. 13 illustrates the continuous frequency signal of a DMRS sequence(Drifted Symbol) and specifically an extended Zadoff-Chu sequence (EZC).FIG. 14 illustrates the corresponding bias of the FO estimator. FIG. 13shows the constant amplitude property of such sequence does not holdtrue between the sub-carrier centre positions located at integermultiples of 15 kHz. Thus FIG. 14 does not illustrate a constant gainacross the frequency range. Thus a frequency offset estimator isrequired.

The metric gain is a function of the sequence including the EZC indexand cyclic shift and the number of allocated sub-carriers G(S,NSC,δf):

$\begin{matrix}{{G\left( {S,N_{SC},{\delta \; f}} \right)} = {\overset{N_{sc} - 1}{\sum\limits_{k = 0}}{{S\left( {k,{\delta \; f}} \right)}{S^{*}\left( {k,{\delta \; f}} \right)}}}} & (27)\end{matrix}$

and can be compensated for in the estimator metric as follows:

$\begin{matrix}{{M\left( {\delta \; f} \right)} = {\sqrt{G\left( {S,N_{SC},{\delta \; f}} \right)}{{\sum\limits_{k = 0}^{N_{sc} - 1}{{R_{S}(k)}{S^{*}\left( {k,{\delta \; f}} \right)}}}}}} & (28)\end{matrix}$

or as follows:

$\begin{matrix}{{M\left( {\delta \; f} \right)} = {\frac{{\sum\limits_{k = 0}^{N_{sc} - 1}{{R_{S}(k)}{S^{*}\left( {k,{\delta \; f}} \right)}}}}{\sqrt{G\left( {S,N_{SC},{\delta \; f}} \right)}} = \frac{{\sum\limits_{k = 0}^{N_{sc} - 1}{{R_{S}(k)}{S^{*}\left( {k,{\delta \; f}} \right)}}}}{\sqrt{\sum\limits_{k = 0}^{N_{sc} - 1}{{S\left( {k,{\delta \; f}} \right)}}}}}} & (29)\end{matrix}$

The resulting metric is no longer biased. This can be mathematicallyverified by checking that it is always maximum at the received frequencyoffset:

$\begin{matrix}{\frac{{M\left( {\delta \; f} \right)}}{{\delta}\; f}{_{{\delta \; f} = {\delta \; f_{u}}}{= 0}}} & (30)\end{matrix}$

where: δf_(u) is the frequency offset of the received sequence R_(S)(k).

FIG. 15 illustrates the resulting residual bias of the associatedestimator, which is now only due to the quantization of the searchedfrequency space (frequency bins). In the case of no sequence hopping orif sequence hopping leads to a reduced set of expected sequences per UE,the gain compensation factor √{square root over (G)} in equation (27)can be incorporated in the frequency bins S*(k,δf) stored in LUT.

The maximum likelihood metric assumes a flat channel across theallocated sub-carriers of a given UE. This is not the case under fadingconditions especially for large allocation sizes. Equalizing thede-mapped sub-carriers R_(S)(k) with the frequency-domain channelestimates Ĥ(k) before frequency estimation circumvents this issue asfollows:

R _(S−eq)(k)=R _(S)(k)Ĥ(k)  (31)

Using the simplest channel estimation derived from weighting thereceived de-mapped samples with the complex conjugate of the expectedfrequency-domain DMRS sequence is:

Ĥ(k)=R _(S)(k)S*(k)  (32)

As a result, the metric is now upgraded to apply to fading channels asfollows:

$\begin{matrix}{{M\left( {\delta \; f} \right)} = {\sqrt{G\left( {S,N_{SC},{\delta \; f}} \right)}{{\sum\limits_{k = 0}^{N_{sc} - 1}{{{R_{S}(k)}}^{2}{S\left( {k,0} \right)}{S^{*}\left( {k,{\delta \; f}} \right)}}}}}} & (33)\end{matrix}$

The metric of equation (33) only operates on DMRS symbols and isaccumulated over antennas, slots and sub-frames as follows:

$\begin{matrix}{\mspace{79mu} {{{M\left( {S_{f},{\delta \; f}} \right)} = {\sum\limits_{s_{f} = 1}^{S_{f}}{\sum\limits_{a = 1}^{N_{a}}{\sum\limits_{s_{l} = 1}^{2}{{m\left( {a,s_{l},s_{f},N_{SC},{\delta \; f}} \right)}\mspace{14mu} {with}}}}}}{{m\left( {a,s_{l},s_{f},N_{SC},{\delta \; f}} \right)} = {{\begin{matrix}{\sum\limits_{k = 0}^{N_{sc} - 1}{{R_{DMRS}\left( {{k + k_{0}},a,s_{l},s_{f}} \right)}}^{2}} \\{S\left( {k,s_{l},s_{f},0} \right){S^{*}\left( {k,s_{l},s_{f},{\delta \; f}} \right)}}\end{matrix}}\sqrt{G\left( {s_{l},s_{f},N_{SC},{\delta \; f}} \right)}}}}} & (34)\end{matrix}$

where: δf is the frequency offset hypothesis; S_(f) is the estimationinterval duration in sub-frames; k is the sub-carrier index; s_(l) isthe slot index; a is the antenna index; s_(f) is the sub-frame index; S(. . . , δf) is the frequency shifted replica of the DMRS sequenceexpected in slot s_(l) of sub-frame s_(f), and computed according toequations (1) and (2); R_(DMRS)( . . . ) is the FFT samples of the DMRSsymbol of slot s_(l) in sub-frame s_(f) from antenna a; G is the gaincompensation factor of equation (27); and N_(SC) is the number ofallocated sub-carriers starting from sub-carrier k₀.

The resulting frequency estimator for this estimation interval is:

$\begin{matrix}{{\hat{\Delta}\; {f\left( S_{f} \right)}} = {\underset{\delta \; f}{\arg \mspace{14mu} \max}\left\{ {M\left( {S_{f},{\delta \; f}} \right)} \right\}}} & (35) \\{{\hat{H}(k)} = {{R_{S}(k)}{S^{*}(k)}}} & (36)\end{matrix}$

As a result, the metric is now upgraded to apply to fading channels asfollows:

$\begin{matrix}\begin{matrix}{{M\left( {\delta \; f} \right)} = \frac{{\sum\limits_{k = 0}^{N_{sc} - 1}{{R_{S}(k)}\overset{\overset{\begin{matrix}\begin{matrix}{{channel}\mspace{14mu} {estimates}} \\{{for}\mspace{14mu} {fading}}\end{matrix} \\{channel}\end{matrix}}{}}{\left\lbrack {{R_{S}(k)}{S^{*}\left( {k,0} \right)}} \right\rbrack^{*}}{S^{*}\left( {k,{\delta \; f}} \right)}}}}{\sqrt{\sum\limits_{k = 0}^{N_{sc} - 1}{{S\left( {k,{\delta \; f}} \right)}{S^{*}\left( {k,{\delta \; f}} \right)}}}}} \\{= \frac{{\overset{N_{sc} - 1}{\sum\limits_{k = 0}}{{{R_{S}(k)}}^{2}{S\left( {k,0} \right)}{S^{*}\left( {k,{\delta \; f}} \right)}}}}{\sqrt{\sum\limits_{k = 0}^{N_{sc} - 1}{{S\left( {k,{\delta \; f}} \right)}}^{2}}}}\end{matrix} & (37)\end{matrix}$

This is referred to as the frequency-bins with common channel estimationmethod. The method of equation (29) is referred to as the frequency-binswithout channel estimation method.

The estimator of equation (37) is biased even without fading because theintroduced channel estimate term R_(S)(k)S*(k,0) has a non-constant gainacross the frequency offset range of the received sequence R_(S)(k).This is fixed by estimating the channel specifically for each frequencyhypothesis δf and normalizing the resulting metric as follows:

$\begin{matrix}\begin{matrix}{{M\left( {\delta \; f} \right)} = \frac{{\sum\limits_{k = 0}^{N_{sc} - 1}{{R_{S}(k)}\overset{\overset{\begin{matrix}\begin{matrix}{{frequency}\text{-}{specific}} \\{{channel}\mspace{14mu} {estimates}}\end{matrix} \\{{for}\mspace{14mu} {fading}\mspace{14mu} {channel}}\end{matrix}}{}}{\left\lbrack {{R_{S}(k)}{S^{*}\left( {k,{\delta \; f}} \right)}} \right\rbrack^{*}}{S^{*}\left( {k,{\delta \; f}} \right)}}}}{\sqrt{\sum\limits_{k = 0}^{N_{sc} - 1}\left\lbrack {{S\left( {k,{\delta \; f}} \right)}{S^{*}\left( {k,{\delta \; f}} \right)}} \right\rbrack^{2}}}} \\{= \frac{\overset{N_{sc} - 1}{\sum\limits_{k = 0}}{{{R_{S}(k)}}^{2}{{S\left( {k,{\delta \; f}} \right)}}^{2}}}{\sqrt{\sum\limits_{k = 0}^{N_{sc} - 1}{{S\left( {k,{\delta \; f}} \right)}}^{4}}}}\end{matrix} & (38)\end{matrix}$

This is referred to as the frequency-bins with per-bin channelestimation method.

One concern with this frequency-bin approach is the complexityassociated with the number of bins needed to cover a sufficientfrequency range with an adequate granularity. This can be solved byrestricting the number of bins to only three in the searched frequencywindow: [−f_(max), 0, f_(max)] and using a parabolic interpolation tolocate the position of the metric maximum. FIGS. 16 and 17 illustratethat both the frequency-bins with common channel estimation method forequation (37) or the frequency-bins with per-bin channel estimationmethod of equation (38) can be mapped onto a parabola.

Three Cartesian points (x_(i), y_(i)) for i=1, 2, 3 where y_(i)=ax_(i)²+bx_(i)+c, the abscissa x_(max) of the maximum y_(max) of the parabolais given by:

$\begin{matrix}{x_{\max} = {\frac{1}{2}\left\lbrack {x_{1} + x_{2} - \frac{\left( {x_{1} - x_{3}} \right)\left( {x_{3} - x_{2}} \right)\left( {y_{1} - y_{2}} \right)}{{\left( {y_{1} - y_{3}} \right)\left( {x_{1} - x_{2}} \right)} - {\left( {y_{1} - y_{2}} \right)\left( {x_{1} - x_{3}} \right)}}} \right\rbrack}} & (39)\end{matrix}$

This reduces significantly the complexity of the frequency-bin approachand makes it a viable alternative to correlation-based approaches.

The frequency range covered by the frequency bins is constant during anestimation interval to allow for consistent accumulation of the metricsof equations (37) and (38). Dynamic control across estimation intervalsnarrows down, when possible, the scope of the searched frequency offset.Empirical simulations identified the following frequency windowadaptation scheme:

$\begin{matrix}\left\{ \begin{matrix}{{f_{searched} \in \begin{bmatrix}{- f_{\max}} & f_{\max}\end{bmatrix}}\mspace{230mu}} \\{{{with}\mspace{14mu} f_{\max}} = {\min \left\{ {{200\mspace{14mu} {Hz}};{\max \left\{ {{2000\mspace{14mu} {Hz}};{3\hat{\delta \; f}}} \right\}}} \right\}}}\end{matrix} \right. & (40)\end{matrix}$

where: δf is the residual frequency estimate of the previous estimationinterval.

The metrics of equations (37) and (38) involve the power of the receivedfrequency domain samples. This results in a sub-optimal estimator sincesquaring increases the estimator variance. In another embodiment of thisinvention a novel metric expression for frequency offset estimationmitigates the estimator variance increase using absolute values insteadof powers. A normalization function maintains a normalized gainproviding a non-biased estimator as follows:

$\begin{matrix}{{M\left( {\delta \; f} \right)} = \frac{\sum\limits_{k = 0}^{N_{sc} - 1}{{{R_{S}(k)}}{{S\left( {k,{\delta \; f}} \right)}}}}{\sqrt{\sum\limits_{k = 0}^{N_{sc} - 1}{{S\left( {k,{\delta \; f}} \right)}}^{2}}}} & (41)\end{matrix}$

This method is referred to as frequency-bins with min-variance per-binchannel estimation. This approach also reduces the complexity as theabsolute value |z| of z=x+j*y is accurately approximated as follows. Leta=max(|x|, |y|) and b=min(|x|, |y|). If b>a/4, |z|=0.875*a+0.5*b.Otherwise, |z|=a. Thus computation of equation (41) requires 4additions/subtractions in 2's complement arithmetic.

FIG. 18 is a flow chart 1800 illustrating the complete frequency offsetestimation and compensation algorithm. Flow chare 1800 begins withinitialization of the data for all UEs and n_(slot) in step 1801. Step1801 computes and stores the value of γ(k, δf, n_(slot), N_(SC)) for allfrequency bins. Step 1803 sets n_(symb) to zero. Step 1804 sets n_(ant)to zero. Step 1805 performs a Fast Fourier Transform of the next symbol.Step 1806 sets n_(symb) to zero. Step 1807 demaps the symbol of UEn_(UE). Step 1808 performs a frequency offset (FO) removal of the symbolproducing R_(S)(n_(UE)). Step 1809 tests to determine if the currentsymbol is a DMRS symbol. If this is true (Yes at step 1809), then step1810 calculates Γ(n_(UE),δf_(i)) for all frequency bins δf_(i). Flowthen advances to step 1811. If this is not true (No at step 1809), thenflow advances to step 1811. Step 1811 increments n_(UE). Step 1812 teststo determine if n_(UE) equals the number N_(b) of UEs. If not true (Noat step 1812), flow loops back to step 1807. If true (Yes at step 1812),the flow advances to step 1813. Step 1813 increments n_(ant). Step 1814tests to determine if n_(ant) equals the number N_(b) of antennas. Ifnot true (No at step 1814), flow loops back to step 1805. If true (Yesat step 1814), the flow advances to step 1815. Step 1815 incrementsn_(symb). Step 1816 tests to determine if n_(symb) equals seven. If nottrue (No at step 1816), flow loops back to step 1804. If true (Yes atstep 1816), the flow advances to step 1817. Step 1817 incrementsn_(slot). Step 1818 tests to determine if n_(slot) equals twiceN_(subframes). If not true (No at step 1818), flow loops back to step1802. If true (Yes at step 1819), the flow advances to step 1819. Step1819 completes the calculation of the frequency offset for all UEs.

FIG. 18 illustrates the scheduling of the functions involved with thefrequency-bin based estimators. The difference between the variousestimators is the metric used and the maximum argument algorithm. Thismaximum argument algorithm could be a basic maximum or a parabolicinterpolation. More specifically, the set of coefficientsγ(k,δf,n_(slot),N_(sc)) is given by:

$\begin{matrix}\left\{ {\quad\begin{matrix}{{{\gamma \left( {k,{\delta \; f},n_{slot},N_{sc}} \right)} = \frac{{S\left( {k,0} \right)}{S^{*}\left( {k,{\delta \; f}} \right)}}{\sqrt{\sum\limits_{k = 0}^{N_{sc} - 1}{{S\left( {k,{\delta \; f}} \right)}}^{2}}}};{{common}\mspace{14mu} {channel}\mspace{14mu} {estimate}}} \\{{{\gamma \left( {k,{\delta \; f},n_{slot},N_{sc}} \right)} = \frac{{{S\left( {k,{\delta \; f}} \right)}}^{2}}{\sqrt{\sum\limits_{k = 0}^{N_{sc} - 1}{{S\left( {k,{\delta \; f}} \right)}}^{4}}}};{{per}\mspace{14mu} {bin}\mspace{14mu} {channel}\mspace{14mu} {estimate}}}\end{matrix}} \right. & (42)\end{matrix}$

The duration of each estimation interval is controlled dynamically via astopping criterion. This stopping criterion is the standard deviation ofthe elementary estimates {circumflex over (Δ)}f(S_(f)−L+1), {circumflexover (Δ)}f(S_(f)−L+2), . . . , {circumflex over (Δ)}f(S_(f)) in anL-length sliding window ending on the last estimate {circumflex over(Δ)}f(S_(f)) of the current interval. FIG. 19 illustrates the timebehavior of the frequency elementary estimates within an estimationinterval obtained from simulation.

The value of the standard deviation threshold σ_(thresh) used asstopping criterion is optimized using simulations. A link-levelsimulator with ideal frequency offset compensation with only one UE, notiming errors and the a varying number of allocated RBs. The averagedurations in number of sub-frames of the estimation interval for variousvalues of the stopping criterion σ_(thresh) Beyond σ_(thresh)=50 Hz theestimation interval duration does not improve further and remains atabout 30 sub-frames.

The BLER performance of the PUSCH with 2 RB allocations for variousvalues of the stopping criterion σ_(thresh) using QPSK and 16QAMmodulation varies. Using the largest value of σ_(thresh) of 50 Hz doesnot degrade the BLER compared to smaller values. As a resultσ_(thresh)=50 Hz minimizes the estimation interval duration to 30sub-frames while achieving high performance BLER for both QPSK and 16QAMmodulations.

The frequency range covered by the frequency bins is constant during anestimation interval to allow for consistent accumulation of the metricof equation (34). The frequency range is dynamically controlled acrossestimation intervals in order to narrow down when possible the scope ofthe searched frequency offset. For simplicity the frequency range of thefrequency bins of this invention is preferably limited to fouruncertainty windows: +/−2000 Hz; +/−1000 Hz; +/−500 Hz; and +/−200 Hz.After each estimation interval, the algorithm selects the smalleruncertainty window not exceeding three times the last estimatedfrequency offset. The preferred embodiment of this invention uses 100frequency bins regardless the uncertainty window. Note that too fine afrequency granularity is overkill and this number may be reduced toprovide about 20 Hz frequency granularity.

The performance of both the CP-correlation and frequency-bins algorithmsin a realistic multi-user SC-FDMA multiplex with ideal and realfrequency offset compensation was evaluated via simulation. For theCP-correlation algorithm the estimated frequency offset was subtractedfrom the modeled frequency offset of the UE under test. For thefrequency-bins algorithm the estimated frequency offset was compensatedin the receiver. In both cases the simulator models a number of UEs withequal allocation size sharing the total bandwidth. The frequency mappingof the UEs was re-selected randomly every sub-frame and intra sub-framefrequency hopping was enabled. The DMRS sequence of the UEs was selectedrandomly for each new estimation interval but was kept the same withinthe estimation interval by allowing no sequence hopping. The simulatormodeled timing errors of the UEs were chosen randomly within a maximumtime uncertainty window. The other UEs other than the UE under test weregiven random power and frequency offsets within maximum uncertaintywindows. The CP-correlation method was modeled using the same algorithmexcept that equation (34) was used as the accumulated metric and allsymbols of the sub-frame were used in the accumulation. Table 3 listsall parameters of the simulation.

TABLE 3 Parameter Value or range System Bandwidth 5 MHz Number of users6 Number of scheduled RBs 4 MCS QPSK ⅓-16QAM ½ RS sequences EZC withrandom selection of ZC index and cyclic shift across freq estimationintervals Scheduling scheme Frequency hopping, no sequence hoppingwithin frequency estimation interval Frequency estimation CP correlationon all symbols and methods frequency bins on DMRS symbols only Number offrequency bins 100 Frequency search window Initial: +/−2 kHz, then sizedynamically adapted as a function of the estimated frequency σmeasurement interval 5 sub-frames size σ_(thresh) 50 Hz Frequencycompensation Ideal, based on FO estimates, or real method at thereceiver. In the latter case, CP FO compensation is implemented oneither de-mapped CP or full bandwidth CP. Max timing uncertainty +/−0.5μs window Max frequency +/−500 Hz uncertainty window (other UEs) Maxpower offset +/−3 dB uncertainty (other UEs) Channels AWGN, TU6-3 km/h,High Speed Train #3

The following evaluation uses as performance criterions the statisticsof the residual frequency offset error after estimation and compensationand the resulting Block Error Rate (BLER). The following evaluationprovides the statistics of the mean, standard deviation and the sum ofboth so as to reflect the overall performance of theestimator/compensation scheme.

This set of simulations allows assessing the impact of non-orthogonal CPin the CP correlation method. The frequency offsets are initialized to800 Hz for AWGN channels and 300 Hz for TU channels. Then, every newfrequency offset estimate is subtracted from the UEs current frequencyoffset. For both AWGN and TU channels the frequency bin method isinsensitive to synchronization and power errors. This is not the case ofthe CP correlation method which outperforms the frequency bin method inideal synchronization conditions but performs worse as soon as arealistic multiplex is modeled. In this case the frequency bin methodoutperforms the CP correlation method despite working on one instead ofseven symbols per slot.

This set of simulations allows assessing the impact of both thenon-orthogonal CP method and the practical (non-ideal) CP frequencyoffset compensation method. The 3GPP RAN WG#4 specified High Speed Train(HST) scenarios with time-varying frequency offsets specificallyaddressing the high performance frequency tracking requirements of LTEreceivers. These simulations use the third scenario out of the threescenarios. This provides the sharpest frequency variations.

For the CP correlation method, simulations tested both wideband CP andde-mapped CP FO compensation methods. The CP correlation method produceserroneous average estimates at both ends of the Doppler shift and thatcompensating the FO on the wideband CP slightly outperforms thecompensation on the de-mapped CP. Of the three tested methods, only thefrequency bin method allows accurate tracking of the Doppler shifttrajectory. All algorithms but the frequency bins have error floors athigh SNR, where the frequency offset has larger impact on the BLER.

The simulations assessed the performance of the various metricselaborated for the frequency-bin approach including: frequency-binswithout channel estimation; frequency-bins with common channelestimation; and frequency-bins with per-bin channel estimation.

As expected, the metric of equation (29) designed to optimize the AWGNchannel performance outperforms the other metrics as long as an idealSC-FDMA multiplex is achieved. In a realistic multiplex where other UEsalso experience some timing errors within the range tolerated by LTE,frequency errors and power differences, the performance of this metricbecomes worse than the other metrics. Thus the frequency-bins withoutchannel estimation method is not suitable in practice for real systems.The two remaining metrics including the common channel estimation andthe per-bin channel estimation have very similar performance on thestatic AWGN channel and are insensitive to the interference resultingfrom non-ideal multiplexing in all channels. The metrics for the per-binchannel estimation shows better frequency offset tracking than themetric with common channel estimation. This is due to the FO-dependentbias upon AWGN of the former metric which is fixed in the latter metricthus accelerating the convergence when tracking FO variations. On theother hand, the metric with common channel estimation is more robust infading channels. As a result, the preferred embodiment of this inventionuses the metric involving per-bin channel estimation on AWGN channelsand the metric involving common channel estimation on fading channels.

The frequency-bins with per-bin channel estimation metric of equation(38) is used for the AWGN and HST#3 channels and the frequency-bins withcommon channel estimation metric of equation (37) is used for the TU 3km/h channel. The parabolic interpolation method improves theperformance with respect to the brute-force equal-spaced frequency binapproach. This is due to the resulting non-quantized frequency offsetestimate. The parabolic interpolation scheme is quite robust withrespect to a non-interference-free realistic multiplex.

This patent application describes in details the design choices for theLTE frequency offset estimation and compensation, from theoreticalderivations and performance evaluations. In particular, it is shown thatthe state-of-the-art does not satisfactorily addresses the high-endperformance requirements of LTE so that an alternate approach is needed.A maximum-likelihood based solution is provided, taking profit of theavailable frequency-domain interference-free symbols de-mapped (orde-multiplexed) at the output of the FFT of an OFDMA multi-userreceiver.

1. A method of wireless transmission for estimating the carrierfrequency offset in a base station of a received Orthogonal FrequencyDivision Multiplexing (OFDM) transmission from a user equipment (UE)accessing an Orthogonal Frequency Division Multiplexing Access (OFDMA)radio access network, comprising: receiving a transmission from the UEat one of a plurality of antennas at the base station; timede-multiplexing selected OFDM symbols from the OFDM symbol multiplex ofa received sub-frame employing a-priori known sub-carrier modulation ofthe selected symbols; computing the frequency-domain symbols receivedfrom each antenna through a Fast Fourier Transform (FFT); de-mappingfrom the frequency-domain symbols the UEs selected sub-carriers of theOFDMA sub-carrier multiplex for each antenna; computing from eachde-mapped symbol from each antenna N metrics M_(i) for i=1, . . . , N,each associated to a carrier frequency offset hypothesis δf_(i) whereinthe set of carrier hypothesis spans a searched frequency offset window;performing the steps of receiving, time de-multiplexing, computing thefrequency-domain symbols, de-mapping and computing metrics M_(i) onsubsequent received sub-frames from the UE over an estimation intervalduration; non-coherently accumulating across the estimation interval andall antennas the computed metrics M_(i,n) associated to the carrierfrequency offset hypothesis δf_(i) for each carrier frequency offsethypothesis δf_(i); and selecting the carrier frequency offset hypothesiswith largest accumulated metric amplitude as the estimated carrierfrequency offset estimate.
 2. The method of claim 1, wherein: theselected OFDM symbols are demodulation reference OFDM symbols (DMRS)provisioned in support of channel estimation.
 3. The method of claim 1,wherein: the selected OFDM symbols are reconstructed demodulated OFDMsymbols.
 4. The method of claim 1, wherein: the OFDMA symbols are SingleCarrier Frequency Division Multiple Access (SC-FDMA) symbols.
 5. Themethod of claim 1, wherein: the OFDMA symbols are Discrete FourierTransform Orthogonal Frequency Division Multiple Access (DFT-SOFDMA)symbols.
 6. The method of claim 1, wherein: said step of computing theestimator metric M_(i) corresponding to carrier frequency offsethypothesis δf_(i) includes: for each de-mapped sub-carrier k multiplyinga transform of the received de-mapped FFT output sub-carrier sampleR_(S)(k) and a transform of the frequency shifted replica S(k,δf_(i)) ofthe frequency-domain sequence symbol expected on sub-carrier k therebyproducing a product; summing the product across all de-mappedsub-carriers k thereby producing a sum; and dividing the sum by anormalization factor.
 7. The method of claim 6, wherein: thenormalization factor is selected to provide a non-biased estimation. 8.The method of claim 6, wherein: the metric selected for addressingsingle UE in the OFDMA multiplex with AWGN channel wherein: thetransform of the received de-mapped FFT output sub-carrier sampleR_(S)(k) is the identity transform leaving R_(S)(k) unchanged; thetransform of the frequency shifted replica S(k,δf_(i)) is the complexconjugate S(k,δf_(i))* of S(k,δf_(i)); and the normalization factor isthe square root of the sum of across de-mapped sub-carriers of thesquared frequency shifted replica S(k,δf_(i))$\sqrt{\sum\limits_{k = 0}^{N_{sc} - 1}{{S\left( {k,{\delta \; f}} \right)}}^{2}}.$9. The method of claim 6, wherein: the metric selected for multiple UEsin the OFDMA multiplex with fading channel and slow varying frequencyoffset wherein: the transform of the received de-mapped FFT outputsub-carrier sample R_(S)(k) is the square of the absolute value ofR_(S)(k) |R_(s)(k)|²; the transform of the frequency shifted replicaS(k,δf_(i)) is the square of the absolute value of S(k,δf_(i))|(k,δf)|²; and the normalization factor is the square root of the sum ofacross de-mapped sub-carriers of the fourth power frequency shiftedreplica S(k,δf_(i))$\sqrt{\sum\limits_{k = 0}^{N_{sc} - 1}{{S\left( {k,{\delta \; f}} \right)}}^{4}}.$10. The method of claim 6, wherein: the metric selected for addressingmultiple UEs in the OFDMA multiplex with fading channel and fast varyingfrequency offset wherein: the transform of the received de-mapped FFToutput sub-carrier sample R_(S)(k) is the square of the absolute valueof R_(S)(k) |R_(s)(k)|²; the transform of the frequency shifted replicaS(k,δf_(i)) is the square of the absolute value of S(k,δf_(i))|S(k,δf)|²; and the normalization factor is the square root of the sumof across de-mapped sub-carriers of the squared frequency shiftedreplica S(k,δf_(i))$\sqrt{\sum\limits_{k = 0}^{N_{sc} - 1}{{S\left( {k,{\delta \; f}} \right)}}^{4}}.$11. The method of claim 6, wherein: the metric selected for addressingmultiple UEs in the OFDMA multiplex with fading channel and fast varyingfrequency offset wherein: the transform of the received de-mapped FFToutput sub-carrier sample R_(S)(k) is absolute value of R_(S)(k)|R_(s)(k)|; the transform of the frequency shifted replica S(k,δf_(i))is the absolute value of S(k,δf_(i)) |S(k,δf)|; and the normalizationfactor is the square root of the sum of across de-mapped sub-carriers ofthe squared frequency shifted replica S(k,δf_(i))$\sqrt{\sum\limits_{k = 0}^{N_{sc} - 1}{{S\left( {k,{\delta \; f}} \right)}}^{2}}.$12. The method of claim 6, wherein: the frequency shifted replicaS(k,δf_(i)) is constructed in frequency domain using aninterpolation-based frequency-domain frequency offset generationtechnique defined as:${{{Z_{i}\left( {k,ɛ} \right)} = {\sum\limits_{l = 0}^{N_{sc} - 1}{{Z(l)}{C\left( {{l - k},ɛ} \right)}}}};{k = 0}},1,{{\ldots \mspace{14mu} N_{SC}} - 1}$where: N_(SC) is the UE allocation size, in sub-carriers; ε is thenormalized frequency shift: ε=δf/Δf_(sc); Z(l) is the de-mappedfrequency points of the UE corresponding to the N_(SC)-point DFT of theoriginal time-domain samples z(n); C(l-k,ε) is the interpolatorcoefficients; and Z_(i)(k,ε) is the interpolated point from the Z(l)points, and:${C\left( {k,ɛ} \right)} = {{\frac{{\sin \left( {\pi \left( {k + ɛ} \right)} \right)}/N_{FFT}}{\sin \left( {{\pi \left( {k + ɛ} \right)}/N_{FFT}} \right)}^{j\; {\pi {({k + ɛ})}}\frac{N_{FFT} - 1}{N_{FFT}}}} \approx {\sin \; {c\left\lbrack {\pi \left( {k + ɛ} \right)} \right\rbrack}^{{{j\pi}{({k + ɛ})}}\frac{\; {N_{FF} - 1}}{N_{FFT}}}}}$     for  k = −N_(SC) + 1, −N_(SC) + 2, …  0, 1, …  N_(SC) − 1where: N_(FFT) is the FFT size and${\sin \; {c(x)}} = {\frac{\sin (x)}{x}.}$
 13. The method of claim6, wherein: the frequency shifted replicas S(k,δf_(i)) are constructedfrom a frequency domain de-mapped samples Z(k) through a combinedIDFT/DFT as defined below:Z(k,ε)=FFT _(2N) _(SC) ^(<) Z _(p)(n)c _(ε)(n)}; k=0,1, . . . N _(SC)−1;n=0,1, . . . 2N _(SC)−1 where: FFT_(N) is the N-point FFT; z_(p)(n) isthe 2N_(SC)-point IDFT of Z_(p)(k), reflecting a 2× time-domainover-sampling with respect to the original sampling rate of z(n);Z_(p)(k) is a zero-padded extension of Z (k), the de-mapped frequencypoints of the UE, to get a 2N_(SC) length vector:${Z_{p}(k)} = \left\{ \begin{matrix}{{{0;{k = 0}},1,\ldots \mspace{14mu},{N_{SC} - 1}}\mspace{220mu}} \\{{{Z\left( {k - N_{SC}} \right)};{k = N_{SC}}},{N_{SC} + 1},\ldots \mspace{14mu},{{2N_{SC}} - 1}}\end{matrix} \right.$ and c_(ε)(n)=e^(j2πγn) where the equivalentnormalized frequency γ is given by$\gamma = {\frac{1}{2}{\left( {1 + \frac{ɛ}{N_{SC}}} \right).}}$ 14.The method of claim 1, wherein: the number N of frequency hypothesis isrestricted to 3 in the searched frequency offset window [−f_(max) 0f_(max)] by using a parabolic interpolation to locate the position ofthe metric maximum where, given the three Cartesian points (x_(i),y_(i)), i=1, 2, 3 such that y_(i)=a x_(i) ²+b x_(i)+c, the abscissax_(max) of the maximum y_(max) of the parabola is given by:$x_{\max} = {{\frac{1}{2}\left\lbrack {x_{1} + x_{2} - \frac{\left( {x_{1} - x_{3}} \right)\left( {x_{3} - x_{2}} \right)\left( {y_{1} - y_{2}} \right)}{{\left( {y_{1} - y_{3}} \right)\left( {x_{1} - x_{2}} \right)} - {\left( {y_{1} - y_{2}} \right)\left( {x_{1} - x_{3}} \right)}}} \right\rbrack}.}$15. The method of claim 1, wherein: the frequency offset estimateobtained during a previous estimation interval is removed from thereceived OFDM symbols after symbol de-mapping and before metriccomputation during a current estimation interval.
 16. The method ofclaim 15, wherein: the frequency offset estimate is removed from thereceived OFDM symbols using an interpolation-based frequency-domainfrequency offset generation technique defined as:${{{Z_{i}\left( {k,ɛ} \right)} = {\sum\limits_{l = 0}^{N_{sc} - 1}{{Z(l)}{C\left( {{l - k},ɛ} \right)}}}};{k = 0}},1,{{\ldots \mspace{14mu} N_{SC}} - 1}$where: N_(SC) is the UE allocation size, in sub-carriers; ε is thenormalized frequency shift: ε=δf/Δf_(SC); Z(l) is the de-mappedfrequency points of the UE corresponding to the N_(SC)-point DFT of theoriginal time-domain samples z(n); C(l−k,ε) is the interpolatorcoefficients; and Z_(i)(k,ε) is the interpolated point from the Z(l)points, and:${C\left( {k,ɛ} \right)} = {{\frac{{\sin \left( {\pi \left( {k + ɛ} \right)} \right)}/N_{FFT}}{\sin \left( {{\pi \left( {k + ɛ} \right)}/N_{FFT}} \right)}^{j\; {\pi {({k + ɛ})}}\frac{N_{FFT} - 1}{N_{FFT}}}} \approx {\sin \; {c\left\lbrack {\pi \left( {k + ɛ} \right)} \right\rbrack}^{j\; {\pi {({k + ɛ})}}\frac{N_{FFT} - 1}{N_{FFT}}}}}$     for  k = −N_(SC) + 1, −N_(SC) + 2, …  0, 1, …  N_(SC) − 1where: N_(FFT) is the FFT size and${\sin \; {c(x)}} = {\frac{\sin (x)}{x}.}$
 17. The method of claim15, wherein: the frequency offset estimate is removed from the receivedOFDM symbols using a combined IDFT/DFT as defined below:Z(k,ε)=FFT ₂ N _(SC) ^(<) z _(p)(n)c _(ε)(n)}; k=0,1, . . . N _(SC)−1;n=0,1, . . . 2N _(SC)−1 where: FFT_(N) is the N-point FFT; z_(p)(n) isthe 2N_(SC)-point IDFT of Z_(p)(k), reflecting a 2× time-domainover-sampling with respect to the original sampling rate of z(n);Z_(p)(k) is a zero-padded extension of Z (k), the de-mapped frequencypoints of the UE, to get a 2N_(SC) length vector:${Z_{p}(k)} = \left\{ \begin{matrix}{{{0;{k = 0}},1,\ldots \mspace{14mu},{N_{SC} - 1}}\mspace{200mu}} \\{{{Z\left( {k - N_{SC}} \right)};{k = N_{SC}}},{N_{SC} + 1},{{\ldots \mspace{14mu} 2N_{SC}} - 1}}\end{matrix} \right.$ and c_(ε)(n)=e^(j2πγn) where the equivalentnormalized frequency γ is given by$\gamma = {\frac{1}{2}{\left( {1 + \frac{ɛ}{N_{{SC}\;}}} \right).}}$18. The method of claim 1, wherein: a frequency range covered by thefrequency bins of an estimation interval is adjusted across estimationintervals with respect to a last obtained frequency estimation.
 19. Themethod of claim 18, wherein: the frequency offset window is adapted asfollows: $\left\{ {\quad\begin{matrix}{{f_{searched} \in \begin{bmatrix}{- f_{\max}} & f_{\max}\end{bmatrix}}\mspace{230mu}} \\{{{with}\mspace{14mu} f_{\max}} = {\min \left\{ {{200\mspace{14mu} {Hz}};{\max \left\{ {{2000\mspace{14mu} {Hz}};{3\hat{\delta \; f}}} \right\}}} \right\}}}\end{matrix}} \right.$ where: δf is the residual frequency estimate ofthe previous estimation interval.
 20. The method of claim 1, wherein:the estimation intervals have a constant duration.
 21. The method ofclaim 1, wherein: the duration of each estimation interval is controlleddynamically with a stopping criterion involving a measured standarddeviation across elementary estimates of a sliding window at the end ofthe estimation interval.